It was established by Siegel [1]} that if \(r_1,\ldots , r_n\)  denote the eigenvalues of \(R\)  (which are necessarily real greater than or equal to 1)
and we denote by \(d_i\)  the numbers
\(d_i=\log {\frac{1 + \sqrt{r}_i}{1-\sqrt{r}_i}}\) 
